Doctoral Dissertations

Keywords and Phrases

Adjacency Graph; Hyperfine Perturbations; Magic Wavelength; Oscillatory Tails; Polarizability; Van Der Waals and Casimir-Polder Interactions


"We study the long-range interaction between two hydrogen atoms, in both the van der Waals and Casimir-Polder regimes. The retardation regime is reached when the finiteness of the speed of light becomes relevant. Provided that both atoms are in the ground states, the retardation regime is achieved when the interatomic distance, R, is larger than 137 a₀, where a₀ is the Bohr radius.

To study the interaction between two hydrogen atoms in 1S and 2S states, we differentiate three different ranges for the interatomic distance: van der Waals range (a₀ « R « a₀/α, where α is the fine structure constant), the intermediate or Casimir-Polder range (a₀/α « R « ħc/L, where L is the Lamb shift energy), and the very long or Lamb shift range (R » ħc/L). We also study the Dirac-δ perturbation potential acting on the metastable excited states in the context of hyperfine splitting.

The |2P1/2⟩ levels, which are displaced from the reference 2S-levels just by the Lamb shift, make the study of hyperfine resolved 2S-2S system very interesting. Each S and P state have a hyperfine singlet and a triplet. Thus, there are 8-hyperfine states per hydrogen atom and 8 x 8 = 64 states in the two atom system. The Hamiltonian matrix of the quasi-degenerate 2S-2S system is thus a (64 x 64)-matrix. Our treatment, which profits from adjacency graphs, allows us to do the hyperfine-resolved calculation. We examine the evolution of the energy levels in the hyperfine subspaces. We notice that there is a possibility of level crossings in higher dimensional quantum mechanical systems, which is a breakdown of the non-crossing theorem.

For higher excited reference states, we match the scattering amplitude and effective Hamiltonian of the system. In the Lamb-shift range, we find an oscillatory term whose magnitude falls off as R⁻² and dominates the Wick-rotated term, which otherwise has a retarded Casimir-Polder type of interaction"--Abstract, page iii.


Jentschura, Ulrich D.

Committee Member(s)

Madison, Don H.
Schulz, Michael, 1959-
Fischer, Daniel
Mohr, Peter J.



Degree Name

Ph. D. in Physics


National Science Foundation (U.S.)


Missouri University of Science and Technology

Publication Date

Fall 2017


xiii, 291 pages

Note about bibliography

Includes bibliographic references (pages 284-290).


© 2017 Chandra Mani Adhikari, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11208

Electronic OCLC #



Financial support of National Science Foundation (U.S.) PHY-1403973

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